The dark gauge boson can contribute to the anomalous magnetic moment of lepton radiatively, with [1]}, [2]}, [3]}
\(\Delta a^{A^\prime }_{\ell } \ = \ \frac{\alpha \epsilon ^{2}}{2\pi }\int _{0}^{1} {\rm d}z \frac{2z(1-z)^2 m_\ell ^2}{z m_V^2+(1-z)^2 m_\ell ^2}\,,\) 
